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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

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What does the variable 'v' typically represent in a transportation word problem?

Back

In transportation problems, 'v' often represents the number of students or items per vehicle.

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What does the variable 'b' typically represent in a transportation word problem?

Back

In transportation problems, 'b' often represents the number of buses or larger vehicles used.

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How do you solve a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is a real-world example of a system of equations?

Back

A real-world example is determining the number of items sold at different prices to find total revenue.

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What does it mean if two lines in a system of equations are parallel?

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If two lines are parallel, it means there is no solution to the system, as the equations represent lines that never intersect.

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What does it mean if two lines in a system of equations coincide?

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If two lines coincide, it means there are infinitely many solutions, as the equations represent the same line.